Shock-Turbulence Interaction in Variable Density Flows

Abstract

Accurate numerical simulations of shock-turbulence interaction (STI) are conducted by a hybrid monotonicity preserving-compact finite difference scheme for a detailed study of STI in variable density flows. Numerical accuracy of the simulations has been established using a series of grid, particle, and linear interaction approximation (LIA) convergence tests. The results show that for current parameter ranges, turbulence amplification by the normal shock wave is much higher and the reduction in turbulence length scales is more significant when strong density variations exist in STI. The turbulence structure is strongly modified by the shock wave, with a differential distribution of turbulent statistics in regions with different densities. The correlation between rotation and strain is weaker in the multi-fluid case, which is shown to be the result of complex role density plays when the flow passes through the shock wave. Furthermore, a stronger symmetrization of the joint probability density function (PDF) of second and third invariants of the anisotropic velocity gradient tensor (VGT) is observed in the multi-fluid case. Lagrangian dynamics of the VGT and its invariants are studied and the pressure Hessian contributions are shown to be strongly affected by the shock wave and local density, making them important to the flow dynamics and turbulence structure.